Based on two-grid discretizations, local and parallel finite element algorithms are proposed and analyzed for the time-dependent Oseen equations. Using conforming finite element pairs for the spatial discretization and backward Euler scheme for the temporal discretization, the basic idea of the fully discrete finite element algorithms is to approximate the generalized Oseen equations using a coarse grid on the entire domain, and then correct the resulted residual using a fine grid on overlapped subdomains by some local and parallel procedures at each time step. By the theoretical tool of local a priori estimate for the fully discrete finite element solution, error bounds of the approximate solutions from the algorithms are estimated. Numerical results are also given to demonstrate the efficiency of the algorithms.

基于两网格离散化，提出了时域相关的Oseen方程的局部和并行有限元算法并进行了分析。使用相符的有限元对进行空间离散化，并使用后向Euler方案进行时间离散化，完全离散有限元算法的基本思想是在整个域上使用粗糙网格逼近广义Oseen方程，然后校正所得残差在每个时间步通过一些局部和并行过程在重叠子域上使用精细网格。通过对完全离散有限元解进行局部先验估计的理论工具，可以估算算法中近似解的误差范围。数值结果也证明了算法的有效性。